`backprop_succeeds_from_PC`

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module: IndisputableMonolith.Complexity.SAT.Completeness
domain: Complexity
line: 208 · github
papers citing: none yet

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IndisputableMonolith.Complexity.SAT.Completeness on GitHub at line 208.

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 205/-- PC ⇒ backpropagation succeeds (via uniqueness).
 206Note: with the current abstract step semantics, uniqueness alone suffices for success.
 207PC becomes relevant once a concrete BPStep is connected to semantic forcing. -/
 208theorem backprop_succeeds_from_PC {n}
 209    (inputs : Finset (Var n)) (aRef : Assignment n) (φ : CNF n) (H : XORSystem n)
 210    (_hpc : PC inputs aRef φ H)
 211    (huniq : UniqueSolutionXOR { φ := φ, H := H }) :
 212    BackpropSucceeds φ H :=
 213  backprop_succeeds_of_unique φ H huniq
 214
 215end SAT
 216end Complexity
 217end IndisputableMonolith

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